Non-convergent sequences in metric spaces

I need to prove that in any metric space containing more than one point exists a non-convergent sequence. This seems easy enough, but after wrestling with definitions of the metric space and the limit of a sequence I can't seem to produce a proof. Do I need to know more to prove this?

I need to prove that in any metric space containing more than one point exists a non-convergent sequence. This seems easy enough, but after wrestling with definitions of the metric space and the limit of a sequence I can't seem to produce a proof. Do I need to know more to prove this?

Let x,y, be two different points in a metric space. What about the seq. ?